On the profinite rigidity of lattices in higher rank Lie groups. (English) Zbl 1527.22019
Summary: We investigate which higher rank simple Lie groups admit profinitely but not abstractly commensurable lattices. We show that no such examples exist for the complex forms of type \(E_8,F_4\), and \(G_2\). In contrast, there are arbitrarily many such examples in all other higher rank Lie groups, except possibly \(\mathrm{SL}_{2n+1}(\mathbb{R})\), \(\mathrm{SL}_{2n+1}(\mathbb{C})\), \(\mathrm{SL}_n(\mathbb{H})\), or groups of type \(E_6\).
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